Vol. 15, No. 3, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
The Hodge ring of varieties in positive characteristic

Remy van Dobben de Bruyn

Vol. 15 (2021), No. 3, 729–745
Abstract

Let k be a field of positive characteristic. We prove that the only linear relations between the Hodge numbers hi,j(X) = dimHj(X,ΩXi) that hold for every smooth proper variety X over k are the ones given by Serre duality. We also show that the only linear combinations of Hodge numbers that are birational invariants of X are given by the span of the hi,0(X) and the h0,j(X) (and their duals hi,n(X) and hn,j(X)). The corresponding statements for compact Kähler manifolds were proven by Kotschick and Schreieder.

Keywords
algebraic geometry, positive characteristic, Hodge cohomology, de Rham cohomology, Grothendieck ring of varieties, birational invariants
Mathematical Subject Classification 2010
Primary: 14G17
Secondary: 14A10, 14E99, 14F40, 14F99
Milestones
Received: 28 January 2020
Revised: 28 June 2020
Accepted: 7 September 2020
Published: 20 May 2021
Authors
Remy van Dobben de Bruyn
Princeton University
Princeton, NJ
United States
Institute for Advanced Study
Princeton, NJ
United States